A network-theoretic approach for characterizing Mack-mode instability in high-speed boundary layers

Abstract

Here we present a network theory-based approach to investigate the Mack-mode instability signature found in high-speed schlieren data from a Mach 6 laminar boundary layer flow over a $7^\circ$ cone. The data contain instability wave packets in the form of coherent rope-like structures which exhibit intermittency. The intermittency implies that conventional Fourier techniques are not particularly well suited for analysis. Network analysis, which is well known for handling episodic spatio-temporal data in a variety of complex systems, provides an alternate and more suitable framework. Techniques from time-varying spatial proximity networks are applied to the present data. The connected components in the network topology reveal lines of constant phase for coherent wave packets associated with the instability, and localized regions of high schlieren light intensity for intermittent laminar or turbulent flow states. The orientation angle of the connected network components is found to be a suitable metric for identifying components associated with the Mack-mode instability, and that enables detailed characterization of the wavelength and propagation speeds of the instability wave packets. Beyond the characterization exercise, network analysis can provide a powerful framework for understanding the fundamental nature of intermittency and its role in the laminar-to-turbulent flow transition process.